A230701 Number of (n+3) X (1+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

2, 8, 30, 102, 348, 1172, 3956, 13326, 44916, 151338, 509978, 1718408, 5790456, 19511640, 65747178, 221543696, 746521190, 2515502046, 8476319172, 28562083692, 96243740012, 324306077270, 1092792451740, 3682309466130, 12408031373682

Offset: 1

Author

R. H. Hardin, Oct 28 2013

Keywords

• nonn

Comments

Column 1 of A230708.

Examples

			Some solutions for n=2:
..0..x..0..x....0..x..1..x....0..x..0..x....0..x..0..x....0..x..2..x
..x..1..x..1....x..1..x..2....x..1..x..2....x..1..x..2....x..1..x..0
..0..x..2..x....2..x..0..x....2..x..0..x....2..x..1..x....0..x..1..x
..x..2..x..0....x..0..x..2....x..0..x..2....x..0..x..0....x..2..x..0
..1..x..1..x....2..x..1..x....2..x..1..x....2..x..2..x....1..x..2..x
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A230708.

Formula

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 6*a(n-3) + a(n-5).

Empirical g.f.: 2*x*(1 + x) / ((1 - x)*(1 - 2*x - 5*x^2 + x^3 + x^4)). - Colin Barker, Mar 17 2018